Question

Firms A and B are Bertrand duopolists facing market demand, P = 300-Q, where Q = QA+QB, and marginal cost, MC = 68. a)What level of output will each firm will produce? b)What price will each charge? c)Why is this outcome a Nash equilibrium?

Answer 1

a) In the Bertrand duopoly, both firms compete over price. Each firm tries to undercut price against the other firm to capture the market. No firm will set the price below marginal cost since then it will make losses. If either of the firm lowers the price below that of the other firm, the other firm will retaliate with lower prices and this will go on till the price of both firms goes down to the marginal cost. So neither price greater than nor less than marginal cost but equal to it. In the present case, the price charged by each firm P1 = P2 = MC = 68

Inserting it in the demand equation,

300 - Q = 68

Q = 232

Now, since the price charged by both firms is equal, the quantity Q will be equally distributed between the two firms.

So, Q1 = Q2 = Q/2 = 232/2 = 116

b) As discussed in a, each firm will charge price equal to marginal cost . P1 = P2 = MC =68

c) The outcome is a nash equilibrium because a price below MC leads to losses and a price above MC leads to competitive undercutting by both firms till P = MC.